Preflop, I'm betting super-wide here, since he's a nit. I can bet ATC here and be profitable until Villain adjusts.

Flop: Standard c-bet. Nothing to see here.

Turn: Here's where things get interesting. I double barrel, as I've picked up an OESD, and get re-raised. Now, obviously I can't call for pot odds here, but I do have implied odds. When creating a range here, I concluded that the only thing villain is likely to have here is a set. He'd fold 2-pairs like T9, 98 etc. preflop, and 3-bet JJ+ preflop. If he had top pair (AT/KT, I don't see him calling with QT/JT) he would be very unlikely to re-raise the turn. The fact that he's re-raised the turn indicates he's prepared to go broke with his hand. Thus, I only need to call $0.84 to win a big pot if I hit my straight, and I can just check/fold if I miss. Ergo, calling was correct.

However, implied odds and estimating ranges is a difficult concept, so I figured I'd post this hand for evaluation.

I'm folding the turn here. You actually have only 3 outs, because J isn't very good: it gives a board 89TJ, when you only have a 7. You won't get any action, also you shouldn't want it too. And even 6 won't give you the nuts. Your implied odds also not good here, just fold.